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Nonlinear generation of vector beams from
AlGaAs nanoantennas
Rocio Camacho,† Mohsen Rahmani,† Sergey Kruk,† Lei Wang,† Lei Xu,†,‡ Daria
Smirnova,† Alexander Solntsev,† Andrey Miroshnichenko,† Hoe Tan,¶ Fouad
Kaurota,¶ Shagufta Naureen,¶ Kaushal Vora,¶ Luca Carletti,§ Costantino De
Angelis,§ Chennupati Jagadish,¶ Yuri S. Kivshar,† and Dragomir N. Neshev∗,†
†Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian
National University, Canberra ACT 2601, Australia
‡The MOE Key Laboratory of Weak Light Nonlinear Photonics, School of Physics and
TEDA Applied Physics Institute, Nankai University, Tianjin 300457, China
¶Department of Electronic Materials Engineering, Research School of Physics and
Engineering, The Australian National University, Canberra ACT 2601, Australia
§Department of Information Engineering, University of Brescia, Via Branze 38, 25123
Brescia, Italy
E-mail: [email protected]
Abstract
The quest for nanoscale light sources with designer radiation patterns and polar-
ization has motivated the development of nanoantennas that interact strongly with
the incoming light and are able to transform its frequency, radiation and polarization
patterns. Here, we demonstrate dielectric AlGaAs nanoantennas for efficient second
harmonic generation, enabling the control of both directionality and polarization of
1
nonlinear emission. We show that the nanodisk AlGaAs antennas can emit second
harmonic in preferential directions and generate complex vector polarization beams,
including beams with radial polarization. This is enabled by specialized III-V semi-
conductor nanofabrication of quality AlGaAs nanostructures embedded in low-index
material, thus allowing for simultaneous forward and backward nonlinear emission.
Our results represent a fundamental step towards efficient nonlinear nanoscale light
sources, finding important applications in bio-photonic imaging and as elements for
efficient nonlinear holograms.
KEYWORDS: nonlinear optics, second harmonic generation, dielectric nanoantennas, nanopho-
tonics, III-V semiconductors, nanofabrication
In recent years, the use of nanoparticles for photon management at the nanoscale has
attracted enormous interest in the scientific community. Enabling new optical functionalities
at the nanoscale requires nanophotonic components capable of manipulating light locally
and then of re-emitting the energy with on-demand frequency, radiation and polarization
patterns.1 We have thus witnessed the development of a plethora of nanoscale metallic and/or
dielectric photonic components, operating as optical nanoantennas for different applications,
including control of light scattering,2–4 and control of quantum emission,5 such as radiation
pattern6 and polarization.7
However, when active control over the radiation frequency is required, new challenges are
to be faced, as this is locked to the emitter’s transitions and cannot be changed by the exci-
tation. While research is underway to overcome this limitation by realising strong coupling
between the emitter and the antenna,8 a lot more flexibility in the frequency conversion can
be realised through nonlinear interactions between the light and the nanoantennas, includ-
ing nonlinear wave-mixing9–11 and harmonic generation.12,13 Indeed, shaping of the nonlin-
ear fields in the harmonic generation process by plasmonic nanoantennas has been recently
tested.14,15 However, the observed efficiency of the nonlinear frequency conversion remains
small, of the order of ∼ 10−11, despite the implementation of different strategies to boost it,
2
such as resonant coupling,16–20 three-dimensional geometries,13 or hybrid nanoantennas.21
All-dielectric nanoantennas22 have recently been suggested as an important pathway to
enhance the frequency conversion efficiency beyond what is possible with plasmonics.23,24
The negligible resistive losses of dielectric nanoantennas avoid heating problems and allow
excitation at much higher light intensities, which is of paramount importance for the effi-
ciency of nonlinear optical phenomena.25 Indeed, third-harmonic generation (THG) in Si
and Ge antennas has been recently investigated, showing a huge enhancement of the con-
version efficiency by optically pumping near the antenna’s magnetic dipolar23,26 or anapole
resonances.27 Conversion efficiencies of 10−7 (see Ref.23) and 10−6 (see Ref.27,28) have been
achieved experimentally. These results clearly illustrate the potential of all-dielectric nanopar-
ticles for nonlinear nanophotonic applications.
Despite these spectacular achievements, only χ(3) nonlinear effects have been observed in
these platforms, since Si and Ge do not exhibit bulk quadratic optical nonlinearity, because
of their centro-symmetric crystal structure. However, exploiting materials with second-order
nonlinear susceptibilities, such as GaAs and AlGaAs, would intrinsically increase the conver-
sion efficiency due to the lower-order nonlinearity. The nonlinear effects in GaAs nanostruc-
tures have been the subject of continuing research, including SHG in GaAs nanowires,29–31
hybrid GaAs-plasmonic nanoholes,32 GaAs micro-ring resonators on insulator33 and most
recently dielectric nanoantennas and metasurfaces.24,34–36 SHG efficiencies larger than 10−3
have been theoretically predicted for free standing AlGaAs nanoantennas24 and efficien-
cies exceeding ∼ 10−5 have been recently measured in backward scattering for AlGaAs35
and GaAs36 sitting on an oxide layer. However, no experiments to date have tested the
possibility for shaping the radiation and polarization patterns of SHG, including achieving
unidirectional harmonic generation or nonlinear generation of beams of complex polarization.
Here, we obtain efficient second harmonic generation (SHG) from dielectric AlGaAs
nanoantenna, and demonstrate the possibility of shaping the SH radiation pattern in forward
and backward directions, as well as its polarization state. In particular we prove that the
3
SHG emission has a complex spatial distribution of its polarization state, which for a specific
size of the nanoantennas leads to the generation of cylindrical vector beams of radial polar-
ization.37 The properties of our SHG aerials are enabled thanks to a new AlGaAs platform,
which allows for simultaneous forward and backward radiation. Our results demonstrate for
the first time to our knowledge the functional beam and polarization shaping of the nonlin-
ear second harmonic emission from dielectric nanoantennas. This represents a fundamental
step for the manipulation of the angular emission of AlGaAs nanoantennas, which will foster
future studies toward the goal of precision engineering of their nonlinear radiation pattern.
An important strategy to achieve such full control of harmonic radiation is to be able to
fabricate AlGaAs nanoantennas that are accessible from forward and backward directions.
However, the existing fabrication techniques do not allow for this, as they require a non-
transparent III-V handle wafer for direct growth of III-V semiconductors. The growth on
transparent substrates (e.g. glass) is avoided33,35,36 because it results in a high density of
dislocations. Recent works have been devoted to transfer of semiconductor films onto a glass
substrate, followed by the fabrication of micro/nano structures,3,33 however this method does
not allow for fabrication of high resolution nanostructures with smooth surfaces and edges,
which is crucial for the exploration of the bulk SHG from AlGaAs nanoantennas, as our goal.
Here we implemented a novel fabrication procedure of AlGaAs-in-insulator, containing
epitaxial growing technique in conjunction with a bonding procedure to a glass substrate.
Our final sample contains high quality Al0.2Ga0.8As nanodisks partially embedded in trans-
parent Benzocyclobutene (BCB) layer, with equivalent refractive index to glass, on a glass
substrate. Figures 1(a-d) illustrate the fabrication steps (details can be found in Methods).
Electron microscopy images of AlGaAs disks embedded in the BCB and the main sample
can be seen in Figs. 1(e) and 1(f), respectively. Further images on the fabrication steps can
be found in the Supporting Information.
The AlGaAs nanodisks are designed to support Mie-type resonances at both the funda-
mental wave (FW) and the second harmonic (SH). In order to match the excitation of the
4
GaAs AlAsAlGaAs
Surface treatment
BCBGlass Substrate
SiO2
500 nm
Peeling off
Sam
ple
Mai
n Su
bstra
te
GaAs
a
b
c d
e
f
Figure 1: Fabrication procedure for AlGaAs nanoresonators in a transparent me-dia. (a) AlGaAs nanodisks defined on a GaAs wafer via electron beam lithography andsequential etching. SiO2 is used as a mask and AlAs as a buffer layer. (b) Formation ofa non-adhesive surface with Cl2 treatment. Sequential removal of the SiO2 mask and AlAsbuffer layer by HF acid. (c) Coating of a BCB layer followed by curing and bonding it to athin glass substrate. (d) Peeling off the AlGaAs nanoresonators embedded into BCB. SEMimages: (e) top-view of the final sample and (f) side view of the main GaAs wafer.
Mie-resonant modes to the FW and SH frequencies, we fabricate nanodisks of various diame-
ters in the range 340−690 nm at a fixed height of 300 nm. Two sets of samples are fabricated:
(i) arrays of nanodisk antennas (1µm periodicity) for linear optical characterization; and
(ii) single nanodisks (5µm apart) for SHG experiments.
First, we measure the linear transmission spectra of the different arrays, Fig. 2(a) (see de-
tails in Methods). The measured spectra are shown in Fig. 2(b). The two vertical dashed lines
indicate the FW and SH wavelengths. We observe a pronounced size-dependant resonance
at the FW wavelength and multiple resonances at the SH wavelength. This is confirmed by
numerical simulations using the rigorous coupled wave analysis (RCWA) method.38 The cal-
culated zero-order forward scattering spectra are depicted in Fig. 2(c). The experimentally
measured spectra are in a good agreement with our numerical calculations.
In Fig. 2(d) we show the extracted scattering cross-section at the FW for nanodisks of
different diameters (see details in Methods). Dots indicate the experimental measurements
5
Pu
mp
Sc
att
erin
g,
a.u
.
800 1200 16000
1
2
3
4
5
6
Tra
nsm
issi
on
Wavelength, nm
340 390 440 490 540 590 640 690
800 1200 1600
Experimentb Theoryc
d
N a n o d i s k s’ D i a m e t e r s, n m
ExperimentTheory
300 400 500 600 700
Nanoparticle Diameter, nm
ωω
a
Figure 2: Linear spectroscopy of AlGaAs resonant nanoantennas. (a) Schematic oftransmission measurements of an array of nanodisk antennas. (b and c) Transmission spectraof the nanodisk arrays measured experimentally and calculated theoretically, respectively.Different colors correspond to different diameters of the nanodisks. Dashed lines show thespectral positions of the FW and the SH. (d) Linear scattering of nanodisks of differentdiameters at pump wavelength of 1556 nm. Solid line – theoretical calculations, dots –experimental measurements.
and solid curve the numerical simulations. The resonant profile of the linear scattering,
maximized for disk diameters of 400 − 500 nm, is essentially determined by a magnetic
dipole and a weaker electric dipole excitations in the disk, playing a dominant role at the
pump FW wavelength (1556 nm). Some minor contributions of quadrupoles tend to grow
slightly, when increasing the disk radius. At the SH wavelength (778 nm), higher-order
multipoles are excited in the nanodisks. These two resonant conditions at the FW and the
SH wavelength are responsible for SHG enhancement in our nanoantennas. However, a more
sophisticated dependence of the SHG efficiency on the size of the nanodisk is expected when
taking into account the spatial overlaps of the resonant modes at the FW and the SH fields.
While these results are obtained for arrays of nanodisks, the relatively large period of
1µm assures little influence on the nearest neighbour coupling. Although, some red shift in
6
the maximal scattering efficiency can be expected for isolated nanodisks. Therefore, from
these results we can infer the optimal sizes of individual AlGaAs nanodisk to explore for
achieving maximum efficiency of SHG from single nanoantennas.
Next, we use AlGaAs nanoantennas fabricated 5µm apart to be able to detect their
individual nonlinear response, Fig. 3(a). We measure the efficiencies of the SHG in both
forward and backward directions for various sizes of the nanodisks (see details in Methods).
These measurements are only possible due to the transparent and homogeneous surrounding
environment of the AlGaAs nanoantennas enabled by our fabrication. In the experiments
we use linear vertical polarization of pump, which is at 45◦ to the crystalline axes of the
AlGaAs nanodisks in order to maximize the nonlinear tensor component.24,34 The laser beam
of average beam power of ∼ 1 mW is then focused by an infrared objective (NA= 0.85) to
a diffraction limited spot of 2.2µm, resulting in peak intensity of ∼ 7 GW/cm2. Another
visible objective (NA= 0.9) collects the SH from an individual disk in forward direction,
while the focusing objective collects the SH radiation in backward direction. The SH signal
is detected by two cooled CCD cameras, calibrated with a power meter. Further details on
the measurement procedure are given in the Methods section and the experimental setup is
depicted in the Supporting Information. The results of our SHG measurements form a single
AlGaAs nanoantenna of different disk diameters are shown in Fig. 3(b,c). The measured
SH efficiency is shown in Fig. 3(b) and is derived as the sum of the measured forward and
backward SH signals. The overall dependence of the efficiency on the antenna size is complex
due to the large number of higher-order modes existing in the SH frequency band. The most
efficient SHG is observed for the antenna diameter of 490 nm, having conversion efficiency
as high as 0.85× 10−4.
Importantly, as seen in Fig. 3(c), the directionality of the second harmonic emission can
be tailored flexibly by changing the disk size. For example, for disk diameters about 400 nm,
the SH radiation is mostly backward, while for disk diameters 500− 600 nm, the backward
to forward ratio remains close to unity with slight domination of the measured backward SH
7
b
300 400 500 600 7000.0
0.2
0.4
0.6
0.8
1.0
-4SH
G E
fc
ien
cy X
10
Nanoparticle Diameter, nm
ForwardBackward
F+B
300 400 500 600 700
1
2
3
4
5
6
Ba
ckw
ard
to
Fo
rwa
rd R
atio
Disk Diameter, nm
2ωa c
ω
Figure 3: Nonlinear spectroscopy of single nanoantennas. (a) Schematic of the singleantenna experiment. (b) Experimentally measured SHG efficiency (PSH/PFW) from a singlenanodisk of different diameter at pump wavelength of 1556 nm. Blue - forward radiation,red - backward radiation. (c) Backward-to-Forward ratio of the SH.
emission. Note that at larger disk diameters, the backward-to-forward ration peaks again,
however, for these larger disks, the dependence becomes very sensitive to the disk diameter
due to the many higher order multipoles that contribute to the SH scattering. The key
feature of our measurements is that we can characterize the nature of the radiation patterns
in both directions, forwards and backwards, as well as in the transverse momentum, as
recently predicted theoretically in Ref.34 Our data, however, suggest that the experimental
measurement apparatus is capturing only a small portion of the total SH radiated power,
due to the finite numerical aperture of our objectives.
To be able to estimate the total efficiency of the radiated SH power, we model numerically
the nonlinear response of the AlGaAs nanodisks with the use of finite element method solver
of COMSOL Multiphysics in the frequency domain. In our simulations, the disk is assumed
to be embedded into a homogeneous medium with a refractive index equivalent to glass
substrate. The material dispersion of AlGaAs is taken from the COMSOL tabulated data.
The second-order nonlinear susceptibility tensor of the [001] grown AlGaAs, possessing a zinc
blende crystalline structure, contains only off-diagonal elements χ(2)ijk with i 6= j 6= k. Thus,
in the principal-axis system of the crystal, the ith component of the nonlinear polarization
at SH frequency is given by
P(2ω)i = ε0χ
(2)ijkE
(ω)j E
(ω)k . (1)
8
We assume an undepleted pump approximation and follow the two coupled steps24,26,34,35
to calculate the radiated SH power. First, we simulate the linear scattering at the fundamen-
tal wavelength. To emulate the experimental conditions more accurately, the disk is excited
by a focused monochromatic Gaussian beam, polarized along the [110] direction. The bulk
nonlinear polarization (1) induced inside the particle is then employed as a source for the
next electromagnetic simulation at the doubled frequency, to obtain the generated SH field.
We choose the disk size for maximal SH d = 490 nm and calculate the three-dimensional
SH far-field radiation pattern, as shown in Fig. 4(a). The nonlinear scattering is governed by
the interference of an electric quadrupole and higher-order nonlinearly-generated multipoles
(up to l = 4), leading to the suppression of the forward SH radiation, Fig. 4(a). The side,
top and bottom views of this radiation pattern are also show in Figs. 4(b-d), respectively.
The shaded area in Fig. 4(b) depicts the forward and backward collection angles of the SH
signal in our experiments. These collection angles are also indicated by the inner circles in
the forward and backward far-field radiation images in Figs. 4(c,d). Clearly, the collected
energy in the experiment is less than the generated total SH. By integrating the amount of
the SH emitted within the numerical aperture of the objective lenses used in experiment, we
can determine that only about 30% of the total SH energy can be experimentally collected in
forward and backward directions. As such, the total generation efficiency is estimated to be
three times larger than the measured collection efficiency, thus exceeding the record value of
10−4. This high efficiency provides a solid ground for the use of our nonlinear nanoantennas
as functional elements for nonlinear beam and polarization shaping.
Next, we perform experimental study of the radiation patterns. We build back-focal plane
(BFP) images of the SH radiation pattern by adding a pair of confocal lenses between the
objective lenses and the cameras, in both forward and backward directions. In Figs. 5(a,c
- top row) we visualize portions of the radiation diagram captured by the objective lenses
based on their numerical aperture. From these BFP images we can make the important
conclusion that the SH radiation at normal direction (the (0, 0) point of the BFP images)
9
x y
zz
x
NA 0.85
NA 0.9
Top ViewFront View(Forward)
Bottom View(Backward)
min
max
ba с d
NA 0.9
y
0.85
y
x
min
max
pu
mp
NA
1.44 0.9
y
xNA
1.44
Figure 4: (a) Calculated 3D pattern of the Far-field SH radiation. (b) Front view of thepattern. Cones indicate range of angles experimentally accessible with our high-NA objec-tives. (c,d) Top and Bottom view of the radiation pattern (directionality diagrams) of theSH radiation within the experimentally accessible range of angles.
is zero, as recently predicted theoretically.34 Zero SH emission in normal direction here
originates from the symmetry of the nonlinear bulk χ(2) tensor and, thus, is not sensitive to
geometry. As a result, the zero SH emission is observed for all studied AlGaAs nanodisks.
To further support these findings, we also measure THG from the same disks. The third
harmonic relies on χ(3) nonlinear tensor and in contrast to the SH radiation pattern has
radiation maximum in normal directions (see details in the Supporting Information). This is
an important finding when arrays of such SH antennas are considered, as the interference of
the multiple antennas from the array will result in lower efficiency radiation into the zero-th
order SH beam. We also note that surface second-order nonlinearities can in principle result
in normal SH radiation,36 however these are not pronounced in our experiments and the
bulk χ(2) is the dominant nonlinear contribution.
However, what is even more intriguing is the polarization state of the observed far-field
doughnut beam. While most works to date have been focused on the radiation pattern of the
emission, the polarization distribution of the emitted light emitted has never been studied
before. To test the polarization properties of the SH radiation from our nanoantennas, we
perform experimental retrieval of the spatially-resolved polarization states of the BFP im-
ages by using Stokes formalism (see details in Methods). We observe vector-beam formation
10
Experiment
Inclination Ellipticity
Experiment
Inclination Ellipticity
Theory
Inclination Ellipticity
Theory
Inclination Ellipticity
a cb d
00.50.85 0.5 0.85 00.50.9 0.5 0.9
00.5
0.8
50.5
0.8
5
Nu
me
rica
l Ap
ertu
re
F o r w a r d B a c k w a r d
00.5
0.9
0.5
0.9
min max min max
Figure 5: Directionality and polarization diagrams of the second harmonic. Toprow: Directionality diagrams in (a,b) forward and (c,d) backward directions. (a,c) Exper-imental measurements, (b,d) theoretical calculations. Arrows visualize polarization states.Bottom row: Experimentally retrieved (a,b) and theoretically calculated (c,d) polarizationinclination angles and ellipticity for the directionality cases of the top row. The incidentbeam polarization is vertical.
at the SH frequency, as shown with the arrows in Fig. 5(a). In particular, in experiment we
observe nearly-perfect radial polarization of the SH in forward direction. In the backward
direction, the polarization state is more complex with polarization inclination having radial
structure and ellipticity ranging from nearly-circular to linear [Fig. 5(c)]. We also calculate
the polarization of the SH beam numerically [see Figs. 5(b,d)]. While the numerical calcula-
tions predict similar polarization states in forward and backward directions, we observe some
differences between theory and experiment. These can be attributed to the slight nonuni-
formity on the surface of AlGaAs as the BCB does not fully cover the nanodisks as well as
due to possible imperfections in nanofabrication.
The nonlinear generation of the vector beams from our AlGaAs nanoantennas can be
intuitively understood by the excitation of Mie-type multipoles at the SH frequency. In
the simplest exemplary case, the vector beam of radial polarization can be emitted by an
electric dipole oriented along the optical axis of the disk antenna. Indeed in our case, higher-
11
order multipoles are excited at the SH wavelength. The superposition of these multipolar
contributions is what governs the output polarisation state, which can be highly nontrivial
and can be engineered for a specific application. Indeed, while in forward direction we
observe polarization close to radial polarization state, the backward polarization state is of
a more general nature.
In summary, we have studied the radiation pattern and polarization state of the SH emis-
sion from AlGaAs nanodisk antennas. We have shown that nonlinear conversion efficiencies
exceeding 10−3 can be achieved, so such antennas can be applied for functional nonlinear
devices at the nanoscale. In particular, nonlinear nanoscale light sources of vector beams
with designer polarisation state, e.g. radial polarization have been experimentally demon-
strated, for the first time to our knowledge. Our results open new avenues for novel nonlinear
imaging,39 as well as application as bright fluorescent markers for bio-imaging, as well as for
design of efficient nonlinear holograms.40
Methods.
Sample fabrication: We used metal-organic chemical vapour deposition (MOCVD) to grow
20 nm AlAs and 300 nm AlGaAs (20% Al fraction) on a GaAs wafer. Patterned SiO2 masks
were fabricated on the AlGaAs layer, using conventional e-beam lithography procedure. SiO2
layer was deposited via Plasma-enhanced chemical vapor deposition (PECVD). Then SiO2
disks were transferred to AlGaAs, AlAs and GaAs by reactive ion etching (RIE) technique.
Subsequently, surface treatment has taken place via Cl2 purging by inductively coupled
plasma (ICP) machine, in order to decrease the adhesion between BCB polymer and GaAs
main wafer. SiO2 masks and AlAs layers were removed by hydrofluoric acid, which resulted
in having AlGaAs disks sitting on GaAs wafer with minimum adhesion. The following step
was the spin coating of 4µm BCB layer on the sample, then curing and bonding it to a
thin glass substrate [see Fig. 1(c)]. Finally, the glass substrate with the BCB layer on top,
12
containing AlGaAs disks, was peeled-off from the main GaAs wafer.
Optical characterization: The transmission through the AlGaAs nanodisk arrays of size
40 × 40µm and periodicity of 1µm was measured using a home-built optical transmission
system with a white-light source (tungsten halogen light bulb) and a spectrometer (Princeton
Instruments Acton SP 2300 monochromator with Andor DU490A-1.7 InGaAs array detec-
tor). The scattering cross-sections were calculated as ln(1 − T ), where T is the measured
transmission, normalised to substrate.
For the SHG experiments, we place a single nanodisk in a focal spot of two confocal air
objective lenses: Olympus LCPlanNIR (0.85 NA, 100× infrared) for focusing of the FW and
Olympus MPlanFLN (0.9 NA, 100× visible) for collection of the SH. We measure a diameter
of the focused pump laser beam by performing knife-edge experiments, and ensure that the
pump beam is close to a diffraction limit of 2.2µm. The substrate side faces the visible
objective. Thus, the objective lens Olympus MPlanFLN collects the SH from an individual
disk in Forward direction, and the lens Olympus LCPlanNIR collects the SH radiation in
Backward direction. The pump laser is a pulsed Er3+-doped fiber laser (∼ 500 fs, repetition
rate of 5 MHz) operating at a wavelength of 1556 nm. At the laser output we employ a
quarter-wave plate and a half-wave plate to control the output polarization. We use two
cooled CCD cameras to detect the SH radiation. In forward direction a notch filter blocks
the pump laser. In backward direction a dichroic mirror is used in front of the objective lens
to direct the backward SH onto the camera.
Acknowledgements
The authors acknowledge the support by the Australian Research Council and participation
in the Erasmus Mundus NANOPHI project, contract number 2013 5659/002-001. We thank
Igal Brener, Giuseppe Leo, and Isabelle Staude for the useful discussions. The authors
acknowledge the use of the Australian National Fabrication Facility (ANFF), the ACT Node.
13
References
(1) Novotny, L.; van Hulst, N. Nat Photon 2011, 5, 83–90.
(2) Fu, Y. H.; Kuznetsov, A. I.; Miroshnichenko, A. E.; Yu, Y. F.; Luk’yanchuk, B. Nat.
Commun. 2013, 4, 1527.
(3) Person, S.; Jain, M.; Lapin, Z.; Senz, J. J.; Wicks, G.; Novotny, L. Nano Lett. 2013,
13, 1806–1809.
(4) Staude, I.; Miroshnichenko, A. E.; Decker, M.; Fofang, N. T.; Liu, S.; Gonzales, E.;
Dominguez, J.; Luk, T. S.; Neshev, D. N.; Brener, I.; Kivshar, Y. ACS Nano 2013, 7,
7824–7832.
(5) Giannini, V.; Fernndez-Domnguez, A. I.; Heck, S. C.; Maier, S. A. Chem. Rev. 2011,
111, 3888–3912.
(6) Curto, A. G.; Volpe, G.; Taminiau, T. H.; Kreuzer, M. P.; Quidant, R.; van Hulst, N. F.
Science 2010, 329, 930–933.
(7) Kruk, S. S.; Decker, M.; Staude, I.; Schlecht, S.; Greppmair, M.; Neshev, D. N.;
Kivshar, Y. S. ACS Photon. 2014, 1, 1218–1223.
(8) Eizner, E.; Avayu, O.; Ditcovski, R.; Ellenbogen, T. Nano Lett. 2015, 15, 6215–6221.
(9) Palomba, S.; Novotny, L. Nano Lett. 2009, 9, 3801–3804.
(10) Zhang, Y.; Wen, F.; Zhen, Y.-R.; Nordlander, P.; Halas, N. J. Proc. Nat. Acad. Sci.
2013, 110, 9215–9219.
(11) Zhang, Y.; Zhen, Y.-R.; Neumann, O.; Day, J. K.; Nordlander, P.; Halas, N. J. Nat.
Commun. 2014, 5, 4424.
(12) Lippitz, M.; van Dijk, M. A.; Orrit, M. Nano Lett. 2005, 5, 799–802.
14
(13) Zhang, Y.; Grady, N. K.; Ayala-Orozco, C.; Halas, N. J. Nano Lett 2011, 11, 5519–
5523.
(14) Wolf, D.; Schumacher, T.; Lippitz, M. Nat. Commun. 2016, 7, 10361.
(15) Gennaro, S. D.; Rahmani, M.; Giannini, V.; Aouani, H.; Sidiropoulos, T. P. H.; Navarro-
Ca, M.; Maier, S. A.; Oulton, R. F. Nano Lett. 2016, 10.1021/acs.nanolett.6b02485.
(16) Aouani, H.; Navarro-Cia, M.; Rahmani, M.; Sidiropoulos, T. P. H.; Hong, M.; Oul-
ton, R. F.; Maier, S. A. Nano Lett. 2012, 12, 4997–5002.
(17) Thyagarajan, K.; Rivier, S.; Lovera, A.; Martin, O. J. Opt. Express 2012, 20, 12860–
12865.
(18) Czaplicki, R.; Husu, H.; Siikanen, R.; Makitalo, J.; Kauranen, M.; Laukkanen, J.;
Lehtolahti, J.; Kuittinen, M. Phys. Rev. Lett. 2013, 110, 093902.
(19) Celebrano, M.; Wu, X.; Baselli, M.; Grossmann, S.; Biagioni, P.; Locatelli, A.; De An-
gelis, C.; Cerullo, G.; Osellame, R.; Hecht, B.; Duo, L.; Ciccacci, F.; Finazzi, M. Nat.
Nanotechn. 2015, 10, 412–417.
(20) Metzger, B.; Gui, L.; Fuchs, J.; Floess, D.; Hentschel, M.; Giessen, H. Nano Lett. 2015,
15, 3917–3922.
(21) Grinblat, G.; Rahmani, M.; Cortes, E.; Caldarola, M.; Comedi, D.; Maier, S. A.; Bra-
gas, A. V. Nano Lett. 2014, 14, 6660–6665.
(22) Kuznetsov, A. I.; Miroshnichenko, A. E.; Brongersma, M. L.; Kivshar, Y. S.;
Lukyanchuk, B. Science 2016, in press .
(23) Shcherbakov, M. R.; Neshev, D. N.; Hopkins, B.; Shorokhov, A. S.; Staude, I.; Melik-
Gaykazyan, E. V.; Decker, M.; Ezhov, A. A.; Miroshnichenko, A. E.; Brener, I.;
Fedyanin, A. A.; Kivshar, Y. S. Nano Lett. 2014, 14, 6488–6492.
15
(24) Carletti, L.; Locatelli, A.; Stepanenko, O.; Leo, G.; Angelis, C. D. Opt. Express 2015,
23, 26544–26550.
(25) Kauranen, M.; Zayats, A. V. Nat. Photon. 2012, 6, 737–748.
(26) Smirnova, D. A.; Khanikaev, A. B.; Smirnov, L. A.; Kivshar, Y. S. ACS Photon. 2016,
10.1021/acsphotonics.6b00036.
(27) Grinblat, G.; Li, Y.; Nielsen, M. P.; Oulton, R. F.; Maier, S. A. Nano Lett. 2016, 16,
4635–4640.
(28) Yang, Y.; Wang, W.; Boulesbaa, A.; Kravchenko, I. I.; Briggs, D. P.; Puretzky, A.;
Geohegan, D.; Valentine, J. Nano Lett. 2015, 15, 7388–7393.
(29) Chen, R.; Crankshaw, S.; Tran, T.; Chuang, L. C.; Moewe, M.; Chang-Hasnain, C.
Appl. Phys. Lett. 2010, 96 .
(30) Grange, R.; Brnstrup, G.; Kiometzis, M.; Sergeyev, A.; Richter, J.; Leiterer, C.;
Fritzsche, W.; Gutsche, C.; Lysov, A.; Prost, W.; Tegude, F.-J.; Pertsch, T.; Tnner-
mann, A.; Christiansen, S. Nano Lett. 2012, 12, 5412–5417.
(31) Bautista, G.; Mkitalo, J.; Chen, Y.; Dhaka, V.; Grasso, M.; Karvonen, L.; Jiang, H.;
Huttunen, M. J.; Huhtio, T.; Lipsanen, H.; Kauranen, M. Nano Lett. 2015, 15, 1564–
1569.
(32) Fan, W.; Zhang, S.; Malloy, K. J.; Brueck, S. R. J.; Panoiu, N. C.; Osgood, R. M. Opt.
Express 2006, 14, 9570–9575.
(33) Pu, M.; Ottaviano, L.; Semenova, E.; Yvind, K. Optica 2016, 3, 823–826.
(34) Carletti, L.; Locatelli, A.; Neshev, D.; Angelis, C. D. ACS Photon. 2016, 10.1021/ac-
sphotonics.6b00050.
16
(35) Gili, V. F.; Carletti, L.; Locatelli, A.; Rocco, D.; Finazzi, M.; Ghirardini, L.; Favero, I.;
Gomez, C.; Lemaıtre, A.; Celebrano, M.; Angelis, C. D.; Leo, G. Opt. Express 2016,
24, 15965–15971.
(36) Liu, S.; Keeler, G. A.; yuanmu Yang,; Reno, J. L.; Sinclair, M. B.; Brener, I. Effi-
cient second harmonic generation from GaAs all-dielectric metasurfaces. Conference on
Lasers and Electro-Optics. 2016; p FM2D.6.
(37) Zhan, Q. Adv. Opt. Photon. 2009, 1, 1–57.
(38) Hugonin, J. P.; Lalanne, P. Reticolo software for grating analysis, Institut d’Optique,
Orsay, France (2005).
(39) de Aguiar, H. B.; Gigan, S.; Brasselet, S. ArXiv e-prints 2016, arXiv:1603.07092.
(40) Almeida, E.; Bitton, O.; Prior, Y. ArXiv e-prints 2015, arXiv:1512.07899.
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